1. ## Hypothesis Testing

Hello,
I am looking for any help in clarifying if I am on the right track, or help to put me on the right track. There is only 1 question with my answers for now, and I would really appreciate any input.

Also for the question I have:
-stated the null and alternative hypothesis
-stated the critical region to reject or fail to reject the null
-Identified the test stat
-found the test stat
-stated the conclusion.

The question:

A customer is in need of a large supply of copper tubing that is cut 1.25 meters long. A plumbing supply company guarantees that if you order a specified lenght, you will receive what you ordered within a standard deviation=0.0001. To test the companies guarantee, a sample of 10 pieces of the tubing was taken. The mean length of the tubing was 1.2502 meters. Assume the population is normally distributed.
a)Is there a significant difference in the specified length of the tubing at the 0.01 significance level? Based on your answer, should the customer trust the guarantee?
b)Calculate the p-value at the 0.01 significance level. Is it significant?

Ho: u=1.25 H1: u=/=1.25
Critical region: Fail to reject Ho if the test statistic falls between 2.33 and -2.33. Reject Ho if the test statistic does not fall between 2.33 and -2.33.
z=6.3 with test stat=0.0001
Conclusion: There is not sufficient sample evidence to warrant rejection of the claim that if you order a specified length of pipe, you will receive it within a standard deviation of 0.0001.
a)No, there is not a significant difference in the length of tubing at the 0.01 significance level. The customer should trust the company's guarantee.
b) P-value=0.0002 and it is not significant.

2. So you have [LaTeX ERROR: Convert failed]

Now I could be wrong here, but the manufactures claim is based on the accuracy of their cut. How I see if their cut is not so accurate you will get a variety of tubes shorter and longer than the required length so the average will always be pretty much the same. I reckon that you should have $H_0 : \sigma = 0.0001 \ \ \ \ H_1 : \sigma > 0.0001$.

So want you want is to find c [LaTeX ERROR: Convert failed] note his is a two tailed test.

use to symmetry of the distribution. to get.

[LaTeX ERROR: Convert failed]

then you transform to Z
[LaTeX ERROR: Convert failed]

[LaTeX ERROR: Convert failed]

using tables I get

[LaTeX ERROR: Convert failed]

I'll put some values in now
[LaTeX ERROR: Convert failed]

giving $$c = 1.24974$$
and $$2 \mu - c = 1.25026$$

so if the manufactures claim is true, 99% of the time we should get [LaTeX ERROR: Convert failed]

1.2502 is within the range (only just) so we can trust their claim.

I thought however, that if > was used, its a right tailed test.

Its all so confusing. And what is the c represent?

4. Originally Posted by Thatgirl